Nuclear quadrupole resonance frequencies and relaxation times of 35Cl and 37Cl in solid chlorine have been measured from 4.2 °K to near the melting point. An analysis of the temperature dependence of the nuclear quadrupole resonance frequencies was made using values for three librational mode frequencies determined previously from Raman spectra. The frequency of a fourth mode was predicted from this analysis. The spin–lattice relaxation times were analyzed using the Bayer model extended by Woessner and Gutowsky and using the librational mode frequencies determined from Raman spectra and the temperature dependence of the nuclear quadrupole resonance frequencies.